Prove that relation define on positive integers such as `R = {(x, y): x - y` is divisible by 3, where `x, y in N}` is an equivalence relation.

Show that relation R in Z of integers given by R = {x,y} : x - y is divisible by 5, x , y inZ } is an equivalence relation.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer.Prove that the relation R on the set Z of all integers numbers defined by (x,y)in R hArr x-y is divisible by n, is an equivalence relation on Z .

Prove that the relation R in Z of integers given by: R = {(x, y): 3x - 3y is an integer } is an equivalence relation. [3] If f: RrarrR defined by f(x) = (6- 5x)/7 is an invertible function, find f^-1 .

Prove that the relation R in Z of integers given by: R = {(x, y): 2x - 2y is an integer } is an equivalence relation. [3] If f: RrarrR defined by f(x) = (4- 3x)/5 is an invertible function, find f^-1 .

Prove that the relation R in Z of integers given by: R = {(x, y): x - y is an integer } is an equivalence relation. [3] If f: RrarrR defined by f(x) = (3- 2x)/4 is an invertible function, find f^-1 .

Let R be a relation defined on the set Z of all integers and xRy when x+2y is divisible by 3.then

A relation R is defined on the set of all integers Z Z follows : (x,y) in "R" implies (x,y) is divisible by n Prove that R is an equivalence relation on Z Z .